Regret Bounds: The regret bounds derived by [1]} hold for HedgeMO if and only if the Upper Confidence Bound (UCB) acquisition function is a part of the portfolio of acquisition functions. The regret bounds follow from the work of [2]} who derived cumulative regret bounds for UCB. In essence, the cumulative regret in our case
is bounded by two sublinear terms as for UCB and an additional term which depends on proximity of the chosen point with the test point proposed by UCB. The interested reader is directed to [2]} and [1]} for a description of the exact regret bounds and their derivation.
